Problem: A circle has a radius of $9$. An arc in this circle has a central angle of $\dfrac{11}{9}\pi$ radians. What is the length of the arc? ${18\pi}$ ${\dfrac{11}{9}\pi}$ $\color{#DF0030}{11\pi}$ ${9}$
First, calculate the circumference of the circle. $c = 2\pi r = 2\pi (9) = 18\pi$ The ratio between the arc's central angle $\theta$ and $2 \pi$ radians is equal to the the ratio between the arc length $s$ and the circle's circumference $c$ $\dfrac{\theta}{2 \pi} = \dfrac{s}{c}$ $\dfrac{11}{9}\pi \div 2 \pi = \dfrac{s}{18\pi}$ $\dfrac{11}{18} = \dfrac{s}{18\pi}$ $\dfrac{11}{18} \times 18\pi = s$ $11\pi = s$